Energy
Transformation for Downhill Skiing
A GIF Animation
Downhill skiing is a classic illustration of the relationship
between work and energy. The skiier begins at an elevated position,
thus possessing a large quantity of potential energy (i.e., energy of
vertical position). If starting from rest, the mechanical energy of
the skiier is entirely in the form of potential energy. As the
skiier begins the descent down the hill, potential energy is lost and
kinetic energy (i.e., energy of motion) is gained. As the skiier
loses height (and thus loses potential energy), she gains speed (and
thus gains kinetic energy). Once the skiier reaches the bottom of
the hill, her height reaches a value of 0 meters, indicating a total
depletion of her potential energy. At this point, her speed and
kinetic energy have reached a maximum. This energy state is
maintained until the skiier meets a section of unpacked snow and
skids to a stop under the force of friction. The friction force,
sometimes known as a dissipative force, does work upon the skiier in
order to decrease her total mechanical energy. Thus, as the force of
friction acts over an increasing distance, the quantity of work
increases and the mechanical energy of the skiier is gradually
dissipated. Ultimately, the skiier runs out of energy and comes to a
rest position. Work done by an external force (friction) has served
to change the total mechanical energy of the skiier.
This intricate relationship between work and mechanical energy is
depicted in the animation below.
Along the inclined section of the run, the total mechanical
energy of the skiier is conserved provided that:
- there is a negligible amount of dissipative forces (such as
air resistance and surface friction), and
- the skiier does not utilize her poles to do work and thus
contribute to her total amount of mechanical energy
Provided that these two requirements are meant, there would be
no external forces doing work upon the skiier during the descent down
the hill. The force of gravity and the normal forces would be the
only active forces. While the normal force is an external force, it
does not do work upon the skiier since it acts at a right angle to
the skiier's displacement. In such situations where the angle
between force and displacement is 90-degrees, the force does not do
work upon the skiier. Consequently, the force of gravity is the only
force doing work on the skiier and therefore the total mechanical
energy of the skiier is conserved. Potential energy is transformed
into kinetic energy; and the potential energy lost equals the
kinetic energy which is gained. Overall, the sum of the kinetic and
potential energy remains a constant value.
The numerical values and accompanying bar chart in the
animation above depicts these principles. During the descent down
the hill, the height of the total mechanical energy (TME) bar remains
a constant quantity, indicating the conservation of total mechanical
energy. Furthermore, as the height of the potential energy (PE) bar
decreases, the height of the kinetic energy (KE) bar increases.
Near the end of the run, the skiier encounters the force of
friction. This force acts in the direction opposite the displacement
of the skiier. The angle between the force and the displacement is
180 degrees. Using the equation for work (F*d*cosine 180 degrees),
the amount of work can be calculated. The value calculated from the
above equation is a negative number, indicating that the work done
serves to remove energy from the object. This is why friction is
sometimes referred to as a dissipative force. The amount of
work which is done is equal to the loss of mechanical energy. The
bar chart in the animation above depicts a work (W) bar with a
negative height. As this bar becomes more negative, the
height of the total mechanical energy (TME) bar becomes smaller. By
the end of the animation, the work bar has reached a height of -8
units and the total mechanical energy bar has change its height from
+8 units to 0 units. Thus, the change in height of the total
mechanical energy bar (-8 units) equals the height of the work bar
(-8 units).
For more information on physical descriptions of motion,
visit
The
Physics Classroom. Specific information is available there on the
following topics:
This page was created by
Tom
Henderson of
Glenbrook South
High School.
Comments and suggestions can be sent by e-mail to
Tom
Henderson.
A hearty thanks is due to lab assistant Carl Bobis for his
assistance with the graphics and GIF animation.
This page last updated on 1/28/98.